Rectangular and polar representations of a complex matrix

Leang S. Shieh; Jason S.H. Tsai; Norman P. Coleman

doi:10.1080/00207728708967156

Rectangular and polar representations of a complex matrix

Leang S. Shieh
, Jason S.H. Tsai
, Norman P. Coleman

Department of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper presents some new definitions of the real and imaginary parts and the associated amplitude and phase of a real or complex matrix. Computational methods, which utilize the properties of the matrix sign function and the principal nth root of a complex matrix, are given for finding these quantities. A geometric series method is newly developed for finding the approximant of the matrix-valued function of tan ⁻¹(X), which is the principal branch of the arc tangent of the matrix X. Several illustrative examples are presented.

Original language	English
Pages (from-to)	1825-1838
Number of pages	14
Journal	International Journal of Systems Science
Volume	18
Issue number	10
DOIs	https://doi.org/10.1080/00207728708967156
Publication status	Published - 1987

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Theoretical Computer Science
Computer Science Applications

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10.1080/00207728708967156

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title = "Rectangular and polar representations of a complex matrix",

abstract = "This paper presents some new definitions of the real and imaginary parts and the associated amplitude and phase of a real or complex matrix. Computational methods, which utilize the properties of the matrix sign function and the principal nth root of a complex matrix, are given for finding these quantities. A geometric series method is newly developed for finding the approximant of the matrix-valued function of tan −1(X), which is the principal branch of the arc tangent of the matrix X. Several illustrative examples are presented.",

author = "Shieh, \{Leang S.\} and Tsai, \{Jason S.H.\} and Coleman, \{Norman P.\}",

note = "Funding Information: This work was supported in part by the U.S. Army Research Office, under Contract DAAG 29-83-K-0037, and U.S. Army Missile Command, under Contract DAAH 01-85-C-A 1 1 1.",

year = "1987",

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T1 - Rectangular and polar representations of a complex matrix

AU - Shieh, Leang S.

AU - Tsai, Jason S.H.

AU - Coleman, Norman P.

N1 - Funding Information: This work was supported in part by the U.S. Army Research Office, under Contract DAAG 29-83-K-0037, and U.S. Army Missile Command, under Contract DAAH 01-85-C-A 1 1 1.

PY - 1987

Y1 - 1987

N2 - This paper presents some new definitions of the real and imaginary parts and the associated amplitude and phase of a real or complex matrix. Computational methods, which utilize the properties of the matrix sign function and the principal nth root of a complex matrix, are given for finding these quantities. A geometric series method is newly developed for finding the approximant of the matrix-valued function of tan −1(X), which is the principal branch of the arc tangent of the matrix X. Several illustrative examples are presented.

AB - This paper presents some new definitions of the real and imaginary parts and the associated amplitude and phase of a real or complex matrix. Computational methods, which utilize the properties of the matrix sign function and the principal nth root of a complex matrix, are given for finding these quantities. A geometric series method is newly developed for finding the approximant of the matrix-valued function of tan −1(X), which is the principal branch of the arc tangent of the matrix X. Several illustrative examples are presented.

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DO - 10.1080/00207728708967156

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JO - International Journal of Systems Science

JF - International Journal of Systems Science

IS - 10

ER -

Rectangular and polar representations of a complex matrix

Abstract

All Science Journal Classification (ASJC) codes

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